By Eyke Hüllermeier

Making use of other frameworks of approximate reasoning and reasoning less than uncertainty, particularly probabilistic and fuzzy set-based innovations, this booklet develops formal types of the above inference precept, that's primary to CBR. The case-based approximate reasoning tools therefore got specifically emphasize the heuristic nature of case-based inference and features of uncertainty in CBR.

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In fact, it can hardly be denied that similarity plays an independent role in human reasoning, as do related concepts such as belief and preference. In this sense, the cognitive basis of similarity-based reasoning is clearly undermined when reducing similarity to other concepts. 3 The concept of similarity 37 the above-mentioned sense but, at the same time, rather counter-intuitive. ” This hypothesis is indeed non-trivial, since measures which are ideal and reasonable at the same time need not necessarily exist.

For example, the global monotonicity axiom states that σ(a, a ) < σ(a, a ) ⇒ ∃ ı ∈ {1, . . , n} : σı (aı , aı ) < σı (aı , aı ). for all a, a , a ∈ A. 2. Commonly used similarity measures are often derived from the weighted Euclidean metric 1/2 n ∆ : (a, a ) → ωı · (aı − aı ) 2 . ı=1 This measure obviously assumes numeric attributes. An example of a more general similarity measure is n σ : (a, a ) → 1 − ωı · ∆ı (aı , aı ), ı=1 where ∆ı is a normalized Euclidean distance in the case of numeric attributes and the discrete distance measure (which takes the value 0 if aı = aı and 0 otherwise) in the case of categorical variables (the ωı are non-negative weights such that ω1 + .

Hybrid representations combining different paradigms belong to the relatively recent developments in intelligent systems research. In this connection, it is interesting to mention that CBR (or principles thereof) can well be integrated with other methods. Particularly, the combination of CBR and methods of rule induction has led to several interesting approaches [89, 90, 174, 29]. , for supporting the adaptation task in CBR [246], for assessing similarity measures [14], and for guiding the search and matching process in the retrieval task.

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